9 Answers
9

Writing and storytelling skills: mostly for DMs. Although D&D is different than a static story format, a DM needs a good understanding of plot and character development. This kind of skill could be applied as a novelist, a screenwriter, or an interactive (PC/console) game developer.

Overall literacy level: DMs and players. Honestly, who on earth uses words like "encumbrance" on a daily basis?

Morals/personal development: DMs and players. I found that playing a holy, good character in D&D served a sort of a "role model" function for me at one point in time. Getting a positive reaction from characters in the game-world when doing good made me want to be more like that character. Your mileage may vary.

Organizational skills: DMs. Keeping track of maps, characters, and notes, can be a surprising amount of work.

Misc. skills: (special case). RPG gaming may inspire you to work on interesting side projects. I am currently working on a Shadowrun RPG character creator project in my spare time; my drive to hone my skills and keep up in my craft as a software developer is owed partly to the game.

I find that everyone's first character in a game fits one of two castes: 'Glorified self image' and 'My favorite advantages', and they are not mutually exclusive. Oftentimes this leads to players who can describe their actions with crisp clarity. However, you occasionally get the moments or new archetypes where a player says "I don't have this, but my character does", and it sometimes inspires them to learn about what their character actually does.
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CatLordMar 31 '12 at 20:12

characterization - the ability to codify a character and to play a codified character– Random generation brings the ability to develop a persona from a set of numbers– point or pick building brings the ability to codify a desired character numerically.

Vocal mimicry - many GM's use vocal changes. The more you do it, the better you get at it.

Visualization – LOADS of practice turning mental images into words when GMing,– Lots of practice turning words into visualizations when playing or GMing.

Math

Basic Mathematics: almost all games use addition; many use subtraction, quite a few use multiplication and division; a few use exponents.

Algebra: Even D&D uses basic algebra, the substitution of symbols for as yet undefined numbers

Geometry and Trigonometry: certain sci-fi games make extensive use of geometric and trigonometric principles in their design systems, and mapping out the designs into deckplans is geometry.

Statistics and Probability - the extensive use of randomizers leads many gamers to make a study of probability and statistics.

Artistic

many players draw their characters

many GM's draw maps and illustrations

many players paint miniatures

Historical Research

many games make use of historical settings in whole or part; most such include additional reading lists.

Many games include historical essays, primary sources and secondary sources, some of which are whole cloth fabrication, some are genuine historical work, but all provide experience and exposure to the various kinds of media historians work with, even if it's fabricated.

the ability to turn a list of events into a narrative. Many adventures are in fact just that, a series of events which get turned by the players into a cohesive narrative. Historical writing is the same skill: turning a list of events into a cohesive narrative.

Language Arts

Role Playing is at its heart a verbal medium with a unique lexicon of jargon; all exposure to established systems of jargon makes further language acquisition of jargon and dialect easier.

exposure to technical writing. It's a learned skill being able to comfortably read technical writing, and such writing is used in many RPG's.

exposure to archaic language terms. Many RPGs use terms which have fallen out of the common use in their setting "fluff"... the more archaic terms one is exposed to, the wider one's personal lexicon becomes, and the easier one's ability to comprehend other archaic or pseudo-archaic texts.

manual writing skills

the ability to phsyically write is practiced often, as character sheets are essentially forms filled in by hand in most cases.

writing to fit limited space. Given that most character sheets are forms, people have to adjust their writing to fit the spaces

computer skills

many gamers will take to making their own character sheets and game aids by computer.

computer aided mapping tools for RPGs include several which are very functional 2-D cad systems. Profantasy's Campaign Cartographer 3 is a fairly full featured 2-D CAD; it has very similar input systems to Autocad and Cadintosh.

web research - many games have web-support sites, and many games also lead players to do research online in relation to the subject matter of their games.

Critical Thinking

Many gamers are exposed to multiple games, and this leads them to elucidate what they like and dislike about each.

Many games cause players to make evaluation of their foes before engagement; this, too, is a form of critical thinking.

Many groups discussions before and after sessions amount to a form of critical thinking about the setting and/or GM, and sometimes, about other players performance in session.

+1 for timeliness alone. Coming late is a silly thing to do if it could have easily been avoided.
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GMJoeApr 2 '12 at 6:37

Sometimes you can also learn how to keep a meeting going - perhaps the Agile Scrum method (timeboxes) may be a good thing to use when your players babble? (I'm a babbler myself)
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Lyndsey FergusonApr 2 '12 at 18:26

Imagination: Mostly for DnD-like RPGs. In DnD, your actions are almost limitless. If you can think if it, you can try to do it. If you have a decent DM and good confidence in your rolls, you can achieve remarkable things. Out-of-the-box thinking is critical in almost all of today's well paying jobs.

Focus: If you don't focus on your fight, you'll probably miss some great opportunities. Or the DM will take special interest in you.

Decision-making: In most RPGs, you have to make decisions that will change the course of the story. RPG players soon learn that making informed decisions based on past facts will help them do better decisions in the future.

Ambition: If there's one thing that's clear in RPGs, it's that hard work improves your character. Harder you work, the faster he becomes powerful. Sadly, some players only stick to that philosophy in the game and don't apply it in real life. But it works the same everywhere. Hard work is always rewarding.

The ability to react to unforeseen circumstances rapidly, and not to panic when things go south.

For a GM, this is an even more pronounced asset. The ability to "wing it" without showing it when players attempt something unplanned, comes in very useful in any non-trivial project in work and leisure.

Being well read. It encourages you to research various cultures, technologies, and other topics - I've read up on medieval demographics for D&D, read African explorers' journals for pulp, Japanese myths for Asian-themed games, etc.

Real world rules exploitation. Whether it's health insurance, corporate America, contests, or the IRS, a solid understanding of how to min-max the system contributes to your success!

Lateral Thinking Slightly different to critical thinking. Problems faced in gaming encourage players to look at alternative ways to get around a problem rather than the obvious head on approach. Several times groups of players I've run for or been with have ignored the immovable door and blown a hole in the wall, dug under it, teleported past it or marched off to convince a guard to let them through rather than wasting energy on a direct battering on the door instead.

This does has other knock on effects however, in a LARP when myself and a friend received a brief to "be guards and stall the players" we engaged them in a half hour discussion about the
joys of ferret farming which the players somehow decided was vital to the plot before the GM came back to see why it was taking so long for them to just beat us up...

for a gm, the benefits are the most outstanding, because knowing how to A> Wrangle Cats and B> entertain small children (or the equivalent) is a handy enough skill. It also helps with C> Public Presentation and D> General Social Interactions.

For a player all those skills are still available, but at a slightly lesser clip.

In general I find the use of imagination and creative problem solving to also be useful end results , if terribly hard to quantify.

Primarily I include 3 major skills towards what an RPG offers the players beyond a way to have fun.

Teamwork - In theory this is obvious. Even if the characters are in opposition there is a certain level of cooperative play that is required for a game to be successful.

Critical Thinking - Despite how the stories may leave tons of in game downtime, players must usually do all of their big thinking in a span of minutes.

Applied Learning - A curve that's very much in favor of players new to a game, even if the person has a lot of tactical prowess or cunning, as they figure out the system they learn how the mechanics work for them.